1. Field of the Invention
The present invention relates to a method for analyzing the effects of interposing bubbles at the ship-water interface on reducing the skin-friction of a cruising ship.
2. Description of the Related Art
As a method for reducing skin-friction in a cruising ship, there is an approach of introducing bubbles in the outer surface region of the ship. Many theoretical models for analyzing the effects of bubbles in reducing the skin-friction assume that a void fraction distribution (distribution of bubbles in the boundary layer) is known before calculating various flow parameters in the flow fields surrounding the ship, therefore, it is essential to clarify the mechanism of producing the void fraction distribution to provide an accurate estimation of friction reduction effects. To apply such a friction reduction method to analysis of bubbly flow effects on an actual ship, it becomes necessary to estimate, during the course of computing various parameters in a flow field, the void fraction from a given volume of bubbles being supplied. Therefore, study of void fraction distribution is also critical from the viewpoints of practical application of bubbly flow for reducing the skin-friction.
The present inventors had disclosed an analytical method for obtaining dynamics of bubbles on the hull surface based on the mixing length theory, in a Japanese Patent Application, First Publication, Hei 8-144646. This was followed by a Japanese Patent Application, First Publication, Hei 9-292999, in which a technique was disclosed to simulate the bubble distribution patterns on hull surfaces. It was further disclosed in Japanese Patent Applications, First Publications, Hei 9-142818 and Hei 10-55453 (U.S. patent application Ser. No. 078,950)that a turbulent flow model in the turbulent boundary layer near the hull surface can be constructed by extending the mixing length theory to a bubbly flow field in the turbulent flow model, it offered an analytical methodology to logically explain past experimental results, and demonstrated that the friction reduction effects in different flow fields can be analytically reproduced, by adjusting the operative wall constant .kappa..sub.1 in the wall law for bubbly flow to indicate the bubble mixing length, in accordance with the extent of flow fields, i.e., the thickness of the turbulent boundary layer produced.
However, in the technique disclosed in the aforementioned Japanese Patent Applications, First Publications, Hei 9-142818 and Hei 10-55453, emphasis was on simplifying the analytical process so that there were aspects of the model which were not fully examined in developing the theoretical framework. For example, it was considered that the following points need to be examined more closely in the future.
(1) Although bubble movement in y-direction (gravitational direction) was discussed quantitatively, it has not been made clear why the bubble can be assumed to remain stationary in x-direction (fluid flow direction) of the turbulent flow. Also, a question was unresolved as to the assumption of a constant magnitude of slip. PA1 (2) When introducing an apparent the mixing length change l.sub.mb, it was necessarily, for mathematical simplification, to suppose that either of the two turbulent flow velocities u'.sub.L, v'.sub.L becomes completely zero and the other becomes affected by damping. In other words, a question remained in the assumption that the fluid shear decrement .tau..sub.t caused by a bubble is given by changes in the turbulent stress (Reynolds stress). PA1 (3) Empirically, a wall constant .kappa..sub.1 for bubbly flow (a constant in the wall law when a micro-bubble is present in the turbulent layer) was assumed to decrease in proportion to (.lambda..sub.m /d.sub.b).alpha..sup.2/3, where .lambda..sub.m is an apparent turbulence scale, d.sub.b is a bubble diameter and .alpha. is a local void fraction. But, it was unclear whether the operative wall constant .kappa..sub.1 would be negative at very small d.sub.b, and similarly, whether .kappa..sub.1 would be negative at low .lambda..sub.m. PA1 (4) It was thought reasonable to assume that .lambda..sub.m.varies.v.sub.L /U.sub..tau. (=y/y.sup.+), (proportional to the length of the bottom surface) where v.sub.L is the dynamic viscosity of liquid and U.sub..tau. is a the frictional velocity, but a question remained whether it is reasonable to assume that y/y.sup.+.varies..delta. where .delta. is the thickness of the turbulent boundary layer. PA1 (5) It was assumed that mixing of a bubble reduces friction, but was not certain that this was sufficient. Is there not a need to consider an increment in the shear stress caused by kinetic mass exchange resulting from motion of the bubble?